Processor-sharing queues: some progress in analysis
Queueing Systems: Theory and Applications
The M/G/1 queue with processor sharing and its relation to a feedback queue
Queueing Systems: Theory and Applications
Waiting Time Distributions for Processor-Sharing Systems
Journal of the ACM (JACM)
Statistical bandwidth sharing: a study of congestion at flow level
Proceedings of the 2001 conference on Applications, technologies, architectures, and protocols for computer communications
On a reduced load equivalence for fluid queues under subexponentiality
Queueing Systems: Theory and Applications
Sojourn time asymptotics in the M/G/1 processor sharing queue
Queueing Systems: Theory and Applications
Modeling and analysis of power-tail distributions via classical teletraffic methods
Queueing Systems: Theory and Applications
Analysis of the M/M/1 Queue with Processor Sharing via Spectral Theory
Queueing Systems: Theory and Applications
Modeling Internet backbone traffic at the flow level
IEEE Transactions on Signal Processing
The equivalence between processor sharing and service in random order
Operations Research Letters
On the stability of the multi-queue multi-server processor sharing with limited service
Queueing Systems: Theory and Applications
Processor sharing: A survey of the mathematical theory
Automation and Remote Control
Waiting times for M/M systems under state-dependent processor sharing
Queueing Systems: Theory and Applications
Exact Sojourn Time Distribution in an Online IPTV Recording System
ASMTA '08 Proceedings of the 15th international conference on Analytical and Stochastic Modeling Techniques and Applications
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We give in this paper an algorithm to compute the sojourn time distribution in the processor sharing, single server queue with Poisson arrivals and phase type distributed service times. In a first step, we establish the differential system governing the conditional sojourn times probability distributions in this queue, given the number of customers in the different phases of the PH distribution at the arrival instant of a customer. This differential system is then solved by using a uniformization procedure and an exponential of matrix. The proposed algorithm precisely consists of computing this exponential with a controlled accuracy. This algorithm is then used in practical cases to investigate the impact of the variability of service times on sojourn times and the validity of the so-called reduced service rate (RSR) approximation, when service times in the different phases are highly dissymmetrical. For two-stage PH distributions, we give conjectures on the limiting behavior in terms of an M/M/1 PS queue and provide numerical illustrative examples.